The Matrix Equation $AX + XB = C$
V. Kučera · SIAM Journal on Applied Mathematics · 1974
A comprehensive theory of the matrix linear equation $AX + XB = C$ is presented. The equation is viewed as a vector equation $LX = C$ in the vector space of all $m \times n$ matrices. As the main result, two necessary and sufficient conditions for a solution to exist and a general form of all solutions are established.